Volume 102, Number 11
Historiography of a Very Fast Gas Reaction: A Case History That Spanned about 12 Decades S. H. Bauer Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853 Received May 28, 2002
Contents I. Introduction II. N2O4:NO2 Studies Prior to World War II III. Five Decades of Investigations, Post-World War II IV. Acknowledgment V. Appendix 1: Timeline of Reports on N2O4 ) 2NO2 Kinetics VI. Appendix 2: Impact Tube Experiments VII. References
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I. Introduction Interconversions, whether physical or chemical, generally are not instantaneous but occur over a span of time. That must have been well appreciated by the alchemists. In the transmission of their received knowledge and secret formulas to their apprentices, they must have specified how long as well as how hot their experimental brews needed to be treated. Undoubtedly, they had theories as to why time was a practical parameter. However, there appears to be no record of attempts to quantitate the speed of a chemical conversion until about 1850 when Wilhelmy’s pioneering study on the rates of inversion of cane sugar was published.1 He defined a parameter (now designated a rate constant) and proposed an empirical expression for its temperature dependence. During the following three decades several empirical relations were suggested. van’t Hoff in 1884 and Arrhenius in 1889 proposed the expression currently in general use.2 Measured reaction rates initially played a crucial role in identifying and classifying reaction mechanisms. Diagrams that purport to describe the sequence of changes in atom-atom connectivities induced by chemical conversions must have been proposed soon after chemists began to assign struc-
tures to molecules. The observed dependencies of rates of reaction on reactant concentration was then recognized as significant indicators of these dynamics. However, measurements of rates of reactions, their quantitative dependence on the concentrations of the participating species, and the temperature dependencies of the derived rate constants comprise but one significant component of the collection of data required for the development of a “mechanism”. By now, the criteria for acceptable mechanisms have evolved and considerably tightened. The designation “fast” for a chemical conversion implies a wide range of time scales, each characteristic of a reaction type. Fast associations, in contrast to fast dissociations, were investigated during the early decades of the 20th century. Clearly, such rates can be no faster than reactions between gaseous species that associate at every molecular encounter to generate adducts that have lifetimes greater than several picoseconds (so as to be detectable as a specific entity). Typical examples are recombinations of alkyl radicals,3 reactions of Lewis acids with corresponding bases,4 and the generation of alkalimetal halides when the metal vapors react with halogen gases.5 To measure these very fast bimolecular associations, a variety of ingenious experimental techniques were developed. The designation “fast” to an isomerization or a dissociation has undergone a “shrinking” process over the past decades, starting the 20th century with halftimes of milliseconds and ending with femtoseconds. The latter became possible via the evolution of laser technologies that provided intense localized radiation pulses and the means for controlling and measuring minute time intervals. These were supplemented by the development of analytical devices with highly enhanced sensitivities in species identification and detection.
10.1021/cr0204045 CCC: $39.75 © 2002 American Chemical Society Published on Web 10/22/2002
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This reveiw is restricted to the second group, dissociations [or isomerizations] wherein the parent species is in dynamic equilibrium with its products. Generally, such systems are described by conventional rate equations, expressed in terms of forward and reverse rate processes: kr
A w\ x C; k f
kr
A-B \ wk x A + B f
d[A]/dt ) -kf[A] + kr[C]; d[A-B]/dt ) -kf[A-B] + kr[A][B]
S. H. Bauer was born in Kaunas, Lithuania, on October 12, 1911. His family emigrated to the United States and settled in Chicago, IL. He became a U.S. citizen in 1927. He attended the University of Chicago and was granted the degrees Ph.B (1931) and Ph.D. (1935). There he studied with Profs. T. R. Hogness (his research director), W. D. Harkins, and H. I. Schlesinger. He then spent two years as a postdoctoral fellow at the California Institute of Technology, working with Profs. R. M. Badger and L. Pauling (infrared spectroscopy and electron diffraction). After serving as instructor in fuel technology at the Pennsylvania State University, he was invited to join the chemistry faculty at Cornell University (1939). He was promoted to professor in 1950. He retired from teaching in 1977 but continues with an active research program to the present. Bauer’s publications deal with molecular structure determination by diffraction, EXAFS, and various spectroscopic techniques; measurements of some physical, thermochemical, and kinetic properties of the boranes; kinetics of fast reactions and spectral emissions at high temperatures as studied in shock waves and in chemical laser systems; mechanisms of pyrolysis of energetic materials (nitroalkanes); and models for condensation from supersaturated vapors. He is the author or co-author of 374 publications. Bauer was a Guggenheim Fellow (1949), an NSF Senior Postdoctoral Fellow (1962) at the CNRC and the Weizman Institute, and an NAS Interacademy Exchange Fellow, USSR (1966). In 1979 he receivd an Alexander von Humbold Award to spend 6 months at the Max Planck Institute of Quantum Optics in Garching-Munchen, Germany. In the fall of 1983 he was appointed the first foreign adjunct professor at the Institute of Molecular Science in Okazaki, Japan. He is a fellow of APS and AAAS and a memeber of Sigma Xi, Phi Beta Kappa, and ACS. He served as ACS lecture-tour speaker in 1975, 1976, 1977, 1980, and 1989. He was Sievers Lecturer, USC (1974); Emerson Lecturer, Emory University (1989), and Visiting Professor at North Dakota State University (1974), at University of CaliforniasIrvine (1978), and at University of CaliforniasRiverside (1978). Bauer served as consultant to the Los Alamos National Laboratory, the Argonne National Laboratory, ARCO at the Harvey Technical Center (1945−1985), and at Lockheed California (Skunk-works unit).
It is convenient to divide isomerization or bond dissociation reactions into two broad groups, one for stable species that require substantial activation to twist or fragment a designated bond, and a second of molecules that incorporate fluxional dynamics or a weak bond that is rapidly broken and reformed at ambient temperatures. For the former group the initiation event involves exposure to a source of external energy, such as photons, high-speed electrons, or high-temperature pulses (laser heating or shock compression). Then the time scale is determined by the intrinsic pulse rise time of the energy source and the response time (and sensitivity) of the analytical device. Currently, for complex conversions as well as for simple dissociations, it is possible to follow the separation of fragments on a femtosecond time scale.6 For comparison, interatomic vibrational periods range from tens of femtoseconds, for tightly bound atom pairs, to picoseconds for fluxional oscillations.
However, because both kf and kr are very large, initially every experimental sample is in an equilibrium, time-independent state. Then, any change in relative concentration must be preceded by a perturbation that temporarily displaces the sample as a whole from equilibrium. One measures the rate of return to equilibrium, that is, the “relaxation time” (τ), defined as the time span required for the system to return to 1/e of the displaced magnitude. Experimentally, perturbations have to be repeated for a range of initial concentrations, and from the measured relaxation times one may derive the conventional rate constants, based on an assumed mechanism. Examples of expressions for τ values in terms of k values, for a variety of mechanisms, are cited in most textbooks on chemical kinetics;7 extended treatments are presented in several treatises.8 The rate of an isomerization is determined by the height of the “potential barrier”. For an isomer pair of equal stability that interconvert via unimolecular kinetics, the relaxation time τ ) 1/(2k), with k ≈ 1015 exp(-E/RT). This is predicated under the limiting assumption that intramolecular rotational/vibrational relaxations are faster than the τ values for structural conversion or dissociation.9 Therefore, one should not apply the above expression to τ values of (ω/p) > 5 × 105. The agreement between his computed and observed values is very good. Absorptions for the neat samples are considerably smaller than those reported by H. J. Bauer.34 A second set of curves show sound speeds versus ω/p; the inflection points correspond to the maxima in absorption. Finally, he listed the previously published values for the dissociation rate constant of nitrogen tetraoxide, reduced to 20 °C and unit atmosphere,
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for neat and diluted samples. They range from 0.53 × 105 to 4.5 × 105 s-1; Sessler’s value is 1.7 × 105 s-1. A pulsed oscillator technique for measuring sound transmission in liquids (1956) was extended to gases in the early 1960s and to studies of N2O4:NO2 equilibration rates. A pulsed oscillator was used to generate a burst of sound waves from a crystal or a microphone. Downstream the outputs from a receiving crystal (or microphone) and an amplitudecalibrated oscillator were recorded concurrently. The delays in amplitude of the burst in sound waves that traveled through the medium were thus measured. This development led to more precise data for both absorption and dispersion than was previously possible. Cher36 recorded absorptions as a function of frequency for 78-394 kc/s in neat samples of the reactants and for mixtures diluted with N2, Ar, and CO2 (refer to Figure 4c). He observed that the maxima in absorption increased with increasing concentration of the tetraoxide, were nearly independent of the total pressure, and varied slightly with temperature, from 25 to 45 °C. He reduced these data by assuming a classical unimolecular mechanism, with limiting low- and high-pressure rate constants at 25 °C:
monochromatic radiation provided a novel means for rapidly perturbing chemical systems. Controlled temperature jumps could be produced by absorbed radiation pulses when (a) the laser frequency is absorbed by one of the reactants; (b) the available frequency is absorbed by an admixed chemically inert species that rapidly transfers its excitation (vib f trans; rot) to all of the molecular species present in the volume illuminated by the laser beam; and (c) direct photolysis of one of the reactants (generally in the UV). In 1984 Gozel et al.41 used a TEA laser to irradiate mixtures of N2O4:NO2, Ar, and low levels of SiF4 (which has a strong absorption in the IR, at 1031.5 cm-1). Thus, via method b, he induced temperature jumps of ≈5-10 °C. The consequent rate of production of additional NO2 was followed photometrically by recording its absorption at 400 nm. His measured relaxation times were reduced to association rate constants for a bimolecular process. A typical set of his operating conditions is as follows: 8 bar Ar + 4.9 mbar N2O4:NO2 + 370 µbar SiF4 at -20 °C. He measured relaxation times for a range of pressures of the diluents (Ar, N2, or He) and attempted to follow the kinetics of association in the “falloff” pressure range. The following values were cited for 0.8 bar Ar, for the temperature interval -32 to +14 °C:
k(d)lp ) 4.5 × 106 L/mol‚s
k(a) ) 2.2 × 1011 exp(+2.2 kcal/mol/RT) cm3 mol-1 s-1
and k(d)hp ) 1.7 × 105 s-1 Blend37 used wide-band solid dielectric tranducers and measured sound velocities to an estimated reproducibility of 0.01%. He covered the frequency span from 1 kHz to 1 MHz, over a temperature range from -20 to +60 °C. (For typical data sets refer to Figure 4d.) He derived a relaxation time reduced to 1 atm at 30 °C: τ ) 0.6 µs. In the intervening period Brokaw38 considered the theory of thermal conductivity in reacting gases. He found that experimental values cited for N2O2:NO2 were adequately described by his theory, on the basis of a bimolecular rate constant, at 296 K of k(d)lp ) 5.3 × 106 L/mol‚s. Mathematical models for heat transfer in gas-cooled nuclear reactors, taking into account the kinetics of chemical reactions, were also developed by Tverkovkin et al.39 The use of shock waves to impose a step rise in temperature was tested again in 1970. Zimet,40 working in Wegener’s laboratory, utilized the technique of “fully dispersed” waves, that is, very weak waves with shock speeds between the equilibrium and frozen sound speeds, to measure the dissociation rate of N2O4. Clearly, shock waves generated in conventionally structured shock tubes induce temperature jumps that are too large to be useful for following the kinetic changes in rapidly equilibrating systems with very low energies of activation. Zimet fitted his data to a bimolecular dissociation mechanism, assuming that the activation energy was ≈11 kcal/mol, proposed by Carrington and Davidson.30 His cited pre-exponential factors are 2.2 × 1014 for Ar as a collision partner and 2.9 × 1014 for N2. The development of readily manipulated laser units that emit significant intensities of selected
k(d) ) 3.8 × 1011 exp(-10.8 kcal/mol/RT) s-1 The positive exponential energy for association is not inconsistent with the value proposed by Carrington and Davidson. However, the corresponding magnitude Gozel derived when N2 was the diluent appears to be unacceptable. An extended set of experiments was undertaken by Borrell and co-workers42 to measure, at 298 K, the pressure dependence of the association rate constant. They covered the pressure range 1-207 bar and thus determined the shape of the “falloff” curve. They used method c, that is, 20 ns pulses of a KrF laser, operating at 248.4 nm, to dissociate N2O4, and followed the return to its equilibrium level by recording absorption of the photolized gas at 220 nm. The diluent gas was N2. Although the nascent NO2 molecules are generated in excited electronic states (A or B), these are rapidly quenched (within nanoseconds). At high N2 pressures no significant rise in sample temperature was thus induced. However, at ∼1 bar the released energy generated a small increment in temperature, estimated to be of the order of 0.8 K. Corrections were introduced for the dependence of absorption coefficients on pressure, to the equilibrium constant for the rise in temperature, and for several additional minor factors. Borrell used Troe’s statistical adiabatic channel model48 to calculate resolved energy and angular momentum state specific rate constants. It appears that these have pronounced maxima at very low energies. Their final data are plotted in Figure 5, including a superposed value published by Zimet40 and four values cited by Carrington and Davidson.30 The large pressure range used in these measure-
Historiography of a Very Fast Gas Reaction
Figure 5. Falloff curve for NO2 association rate constants (diluted in N2) at 300 K. The solid curve connects data points measured by Borrell et al. (Appendix 1, entry 26). The point O is the single value reported by Zimet (Appendix 1, entry 23); 2 represent values derived from the first shock tube experiments by Carrington and Davidson (Appendix 1, entry 14).
ments, at 298 K, permitted deriving both the lowand high-pressure limiting values for the association rate constants:
k(a)hpl ) 8.3 × 10-13 cm3 molecule-1 s-1 k(a)lpl ) 1.4 × 10-3 ([N2]) cm6 molecule-2 s-1 Using Troe’s analysis they derived temperaturedependent values for the range 300 < T/K < 600:
k(a)hpl ) 8.3 × 10-13 (300/T)1.1 k(d)hpl ) 7.7 × 10-15 (300/T)1.1 exp (-6460/T) s-1 The relaxation time of N2O4:NO2 subjected to a mild perturbation was also measured by the optoacoustic technique. That radiation pulses in absorbing media generate corresponding sound waves has been known for more than 120 years. A. G. Bell’s empirical tests were described in 1880,44 and concurrently, there appeared reports of laboratory experiments by Ro¨ntgen45 and Tyndall.46 Then 48 years elapsed before Russian investigators used optoacoustics for chemical analysis. Currently, there are 515 citations listed on the World Wide Web that describe optoacoustic devices for measuring a variety of material properties. The sound waves generated via pulsed radiation lag in phase relative to those of exciting radiation. This appears to have been first noted by Slobodskaya,47 who related the phase-lag to the vibrational relaxation time in CO2. Later, Turrell measured the vibrational lifetime of excited CO.48 Vibrational relaxation times in CO2 were remeasured for wet and dry samples for both low and high pressures by Jacox.49 Since then highly improved techniques for generating controlled light pulses, along with increased sensitivity and precision in detecting sound waves, have led to a virtual explosion of applications of optoacoustic devices. For measurements of the relaxation time of nitroxide gases following a thermal perturbation, two variants of the optoacoustic effect were utilized, designated “resonant” and “nonresonant” detection
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Figure 6. Typical resonance curve recorded for the first radial mode of the cylinder used by Fiedler and Hess (Appendix 1, entry 28). Note their partition of contributions from several sources to the overall response curve.
of the sonic signals. These refer to the response of the cell to the minute pressure modulations. In a preliminary investigation Roozendael and Herman50a demonstrated that the populations of rotational levels of NO2 and N2O4 were perturbed by incident pulses of Ar laser radiation (at 488 nm) and that as a consequence rapid but minute jumps in temperature were induced. They described50b a nonresonant optoacoustic probing of the heat dissipation rate in N2O4:NO2 mixtures. Of special note is their introduction of a high-sensitivity condenser-type microphone in their cylindrical acoustic cell. Again, any relaxation process that is slower than the chopping frequency shifts the phase and amplitude of the acoustic signal. Both were measured under a variety conditions for chopping frequencies of 40-320 Hz, in neat samples at 2.2, 3.8, 5.5, and 6.5 Torr. They defined a pressureindependent relaxation time, τ° ) τ/p, and derived τ° ) 5 × 10-5 s/Torr at 25 °C. For the corresponding second-order dissociation rate constant, k°(d)/p, they proposed k°(d) ) 1.5 × 102 s-1/Torr, which reduces to k(d) ) 2.6 × 106 L/mol‚s. A more extended set of measurements was described by Fielder and Hess51 using a resonant acoustic cell. Standing waves were excited by an amplitude-modulated Ar laser, and the sound waves were detected with an electred microphone inserted in the side of a thermally stabilized stainless steel cylinder. Carefully designed optical and electronic components characterize these measurements. They tested neat samples over a range of low pressures, at various temperatures (273-317 K). A detailed theoretical model for such resonators was developed for correlating sound frequency dispersion, absorption, and resonance broadening of the acoustic signals. Figure 6 illustrates the partition of their detector response curve to contributions from several relaxation sources. In a table they compared seven published values for reciprocal relaxation times (1/τ) for neat samples, at 298 K, reduced to 760 Torr, which were derived from sound dispersion or absorption measurements. These range from 1.5 × 105 to 2.3 × 105 s-1. Fielder and Hess favor the lower value. The corresponding bimolecular dissociation rate con-
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stants (reduced to 298 K) range from k(d) ) 8.9 × 10-15 to 4.3 × 10-15 cm3 molecule-1 s-1. Fielder and Hess favor 6.1 × 10-15, an intermediate value. Thus, there is general agreement for magnitudes of kinetics parameters evaluated from acoustic relaxation time measurements, but there is one perturbing value. The activation energy for N2O4 dissociation proposed by Fielder and Hess is 8.6 kcal/mol, which is ∼3 kcal lower than that derived via other techniques. At this stage perhaps one may regard measurements of N2O4:NO2 relaxations via acoustic devices primarily as means to validate the technique rather than for providing firmer values for the relaxation times that characterize that rapidly equilibrating system. It appears that nitrogen tetraoxide is a “strange” compound, not only with respect to its kinetics of dissociation but also with respect to its electronic structure. DFT calculations52 of thermochemical and structural parameters for the five analogous X2N-NX2 species (X ) O, CN, F, CH3, and H) present sharp contrasts between N2O4 and the other four. The N-N bond length in the tetraoxide is 1.78 Å compared to 1.44-1.48 Å in the species with X ) CN, F, CH3, and H. However, the barrier for rotation out of the planar configuration (D2h) was measured to be 1900 cm-1.53 The
